Efficient reasoning with inconsistent information using C-systems

The paper subsumes and extends in a radical way a line of research aimed at automation of reasoning with inconsistent information using paraconsistent logics. We provide a new method for uniform, modular construction of analytic calculi for all major logics in the crucial class of paraconsistent logics known as C-systems. The method is based on semantic characterization of those logics via non-deterministic matrices (Nmatrices), and – unlike that developed previously – is also applicable to C-systems which can only be characterized by infinite Nmatrices. What is more, we show that the results obtained in this paper for infinite semantics imply our earlier results for finite semantics.